We have studied defects and ripples in graphene, dislocation nucleation and motion in crystals, nucleation of bubbles in radioactive waste, aggregation processes to form particles, domain walls and oscillations in semiconductor superlattices.
Graphene is a two dimensional crystal with promising properties. Atoms are arranged forming a honeycomb lattice. We have characterized defects experimentally observed in the atomic lattice as cores of dislocations and dislocation groups: heptagon-pentagon pairs, vacancies, divacancies, Stone-Wales defects… We use periodized discrete elasticity models and singular solutions of elasticity equations to study the dynamical stability of such defects. Our predictions have been corroborated by experimental observations. We have coupled Foppl-Von Karman descriptions of graphene plates to stochastic effects producing domains forming ripples and studying out-of-plane deformations around the core of defects.
Periodized discrete elasticity models allow us to understand dislocation nucleation in cubic crystals during indentation tests in terms of bifurcations. We have shown that bifurcations also characterize the Peierls stresses and depinning transition of such defects, whose motion may be described by travelling wave solutions.
Earlier, we observed a similar depinning transition in experiments of domain wall relocations in semiconductor superlattices. Predictions of thresholds for controlling parameters and of propagation speeds are obtained reducing the dynamics of the whole lattice to a small set of active points.
By asymptotic studies of Becker-Döring type models we have obtained descriptions of particle nucleation and coarsening processes. We performed further studies of bubble formations in the context of radioactive waste.
In all cases, asymptotic and analytical predictions are validated by numerical simulations whose results are then compared to available experimental information. In the course of the simulations, we have developed specific numerical schemes for hyperbolic and kinetic models, as well as also nonreflecting boundary conditions for waves.
| Graphene |
| Measuring strain and rotation fields at the dislocation core in graphene, L.L. Bonilla, A. Carpio, C. Gong, J.H. Warner, Physical Review B 92(15), 155417, 2015 [pdf] [arxiv] Driving dislocations in graphene, L.L. Bonilla, A. Carpio, Science 337(6091), 161-162, 2012 [pdf] Model of ripples in graphene, L.L. Bonilla, A. Carpio, Physical Review B 86(19), 195402, 2012 [pdf] [arxiv] Ripples in a graphene membrane coupled to Glauber spins, L.L. Bonilla, A. Carpio, Journal of Statistical Mechanics- Theory and Experiment, P09015, 2012 [pdf] [archivo] Ripples in a string coupled to Glauber spins, L.L. Bonilla, A. Carpio, A. Prados, R.R. Rosales, Physical Review E 85(3), 031125, 2012 [pdf] [arxiv] Theory of defect dynamics in graphene: defect groupings and their stability, LL Bonilla, A. Carpio, Continuum Mechanics and Thermodynamics 23(4), 337-346, 2011 [pdf] [arxiv] Nonequilibrium dynamics of a fast oscillator coupled to Glauber spins, L.L. Bonilla, A. Prados, A. Carpio, Journal of Statistical Mechanics-Theory and Experiment, P09019, 2010 [pdf] [arxiv] Phase transitions in a mechanical system coupled to Glauber spins, A. Prados, L.L. Bonilla, A. Carpio, Journal of Statistical Mechanics-Theory and Experiment, P06016, 2010 [pdf] [arxiv] Periodized discrete elasticity models for defects in graphene, A. Carpio, L.L. Bonilla, Physical Review B 78(8), 085406, 2008 [pdf] [arxiv] Dislocations in graphene, A. Carpio, L.L. Bonilla, F. de Juan, M.A.H. Vozmediano, New Journal of Physics 10, 053021, 2008 [pdf] |
| Dislocations and plasticity in crystals |
| Nonreflecting boundary conditions for discrete waves, A. Carpio, B. Tapiador, Journal of Computational Physics 229(5), 1879-1896, 2010 [pdf] [archivo] Toy nanoindentation model and incipient plasticity, I. Plans, A. Carpio, L.L. Bonilla, Chaos, solitons and fractals 42(3), 1623-1630, 2009 [pdf] [arxiv] Homogeneous nucleation of dislocations as bifurcations in a periodized discrete elasticity model, I. Plans, A. Carpio, L.L. Bonilla, EPL (Europhysics Letters) 81(3), 36001, 2008 [pdf] [arxiv] Dislocations in cubic crystals described by discrete models, L.L. Bonilla, A. Carpio, I. Plans, Physica A: Statistical Mechanics and its Applications 376, 361-377, 2007 [pdf] [arxiv] Discrete models of dislocations and their motion in cubic crystals, A. Carpio, L.L. Bonilla, Physical Review B 71(13) 134105, 2005 [pdf] [arxiv] Nonlinear stability of oscillatory wave fronts in chains of coupled oscillators, A. Carpio, Physical Review E 69(4), 046601, 2004 [pdf] [arxiv] Oscillatory wave fronts in chains of coupled nonlinear oscillators, A. Carpio, L.L. Bonilla, Physical Review E 67(5), 056621, 2003 [pdf] [arxiv] Edge dislocations in crystal structures considered as travelling waves in discrete models, A. Carpio, L.L. Bonilla, Physical Review Letters 90(13), 135502, 2003; 91(2), 029901 2003 [pdf1] [pdf2] [arxiv] Pile-up solutions for some systems of conservation laws modelling dislocation interaction in crystals, A. Carpio, SJ Chapman, JJL Velazquez, SIAM Journal on Applied Mathematics 61(6), 2168-2199, 2001 [pdf] [arxiv] On the modelling of instabilities in dislocation interaction, A. Carpio, SJ Chapman, Philosophical Magazine B 78(2), 155-157, 1998 [pdf] Dynamics of line singularities, A. Carpio, S.J. Chapman, S.D. Howison, J.R. Ockendon, Philosophical Transactions of the Royal Society A 355 (1731), 2013-2024, 1997 [pdf] [archivo] |
| Nucleation |
| Analysis of helium bubble growth in radioactive waste, A. Carpio, B. Tapiador, Nonlinear Analysis-Real World Applications 11(5), 4174-4184, 2010 [pdf] [archivo] Theory of surface deposition from boundary layers containing condensable vapour and particles, J.C. Neu, A. Carpio, L.L. Bonilla, Journal of Fluid Mechanics 626, 183-210, 2009 [pdf] [arxiv] Kinetics of helium bubble formation in nuclear materials, L.L. Bonilla, A. Carpio, J.C. Neu, W.G. Wolfer, Physica D- Nonlinear Phenomena 222(1-2), 131-140, 2006 [pdf] [arxiv] Asymptotic and numerical studies of the Becker-Döring model for transient homogeneous nucleation, LL Bonilla, A. Carpio, Y. Farjoun, JC Neu, Markov processes and related fields, 12, 341-365, 2006 [arxiv] Igniting homogeneous nucleation, J.C. Neu, L.L. Bonilla, A. Carpio, Physical Review E 71(2), 021601, 2005 [pdf] [arxiv] |
| Semiconductors |
| Self-sustained current oscillations in the kinetic theory of semiconductor superlattices, E. Cebrián, L.L. Bonilla, A. Carpio, Journal of Computational Physics 228(20), 7689-7705, 2009 [pdf] [arxiv] Effects of disorder on the wave front depinning transition in spatially discrete systems, A. Carpio, L.L. Bonilla, A. Luzon, Physical Review E (RC) 65(3), 035207, 2002 [pdf] [arxiv] Numerical study of hyperbolic equations with integral constraints arising in semiconductor theory, A. Carpio, P. Hernando, M. Kindelan, SIAM Journal on Numerical Analysis 39(1), 168-191, 2001 [pdf] [arxiv] Motion of wave fronts in semiconductor superlattices, A. Carpio, LL Bonilla, G. Dell'Acqua, Physical Review E 64(3), 036204, 2001 [pdf] [arxiv] Wave fronts may move upstream in semiconductor superlattices, A. Carpio, LL Bonilla, A Wacker, E Schöll, Physical Review E 61(5), 4866-4876, 2000 [pdf] [arxiv] |
